LMFDB - Embedded newform 216.2.f.b.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(107,216)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("216.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.8
Root			$0.335728 - 1.37379i$ of defining polynomial
Character	$\chi$	$=$	216.107
Dual form			216.2.f.b.107.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35760 + 0.396143i) q^{2} +(1.68614 + 1.07561i) q^{4} -0.505408 q^{5} +3.42703i q^{7} +(1.86301 + 2.12819i) q^{8} +O(q^{10})$	\(q+(1.35760 + 0.396143i) q^{2} +(1.68614 + 1.07561i) q^{4} -0.505408 q^{5} +3.42703i q^{7} +(1.86301 + 2.12819i) q^{8} +(-0.686141 - 0.200214i) q^{10} -3.31662i q^{11} -2.55164i q^{13} +(-1.35760 + 4.65253i) q^{14} +(1.68614 + 3.62725i) q^{16} -5.04868i q^{17} +4.74456 q^{19} +(-0.852189 - 0.543620i) q^{20} +(1.31386 - 4.50264i) q^{22} -6.44121 q^{23} -4.74456 q^{25} +(1.01082 - 3.46410i) q^{26} +(-3.68614 + 5.77846i) q^{28} -5.43039 q^{29} +5.97868i q^{31} +(0.852189 + 5.59230i) q^{32} +(2.00000 - 6.85407i) q^{34} -1.73205i q^{35} -11.1565i q^{37} +(6.44121 + 1.87953i) q^{38} +(-0.941578 - 1.07561i) q^{40} +1.87953i q^{41} -4.00000 q^{43} +(3.56738 - 5.59230i) q^{44} +(-8.74456 - 2.55164i) q^{46} +10.8608 q^{47} -4.74456 q^{49} +(-6.44121 - 1.87953i) q^{50} +(2.74456 - 4.30243i) q^{52} +5.93580 q^{53} +1.67625i q^{55} +(-7.29339 + 6.38458i) q^{56} +(-7.37228 - 2.15121i) q^{58} +6.63325i q^{59} -5.10328i q^{61} +(-2.36841 + 8.11663i) q^{62} +(-1.05842 + 7.92967i) q^{64} +1.28962i q^{65} -4.00000 q^{67} +(5.43039 - 8.51278i) q^{68} +(0.686141 - 2.35143i) q^{70} -4.41957 q^{71} +7.74456 q^{73} +(4.41957 - 15.1460i) q^{74} +(8.00000 + 5.10328i) q^{76} +11.3662 q^{77} +4.30243i q^{79} +(-0.852189 - 1.83324i) q^{80} +(-0.744563 + 2.55164i) q^{82} +3.61158i q^{83} +2.55164i q^{85} +(-5.43039 - 1.58457i) q^{86} +(7.05842 - 6.17889i) q^{88} +17.0256i q^{89} +8.74456 q^{91} +(-10.8608 - 6.92820i) q^{92} +(14.7446 + 4.30243i) q^{94} -2.39794 q^{95} -1.00000 q^{97} +(-6.44121 - 1.87953i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4}+O(q^{10}) $ 8 * q + 2 * q^4	$ 8 q + 2 q^{4} + 6 q^{10} + 2 q^{16} - 8 q^{19} + 22 q^{22} + 8 q^{25} - 18 q^{28} + 16 q^{34} - 42 q^{40} - 32 q^{43} - 24 q^{46} + 8 q^{49} - 24 q^{52} - 36 q^{58} + 26 q^{64} - 32 q^{67} - 6 q^{70} + 16 q^{73} + 64 q^{76} + 40 q^{82} + 22 q^{88} + 24 q^{91} + 72 q^{94} - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 + 6 * q^10 + 2 * q^16 - 8 * q^19 + 22 * q^22 + 8 * q^25 - 18 * q^28 + 16 * q^34 - 42 * q^40 - 32 * q^43 - 24 * q^46 + 8 * q^49 - 24 * q^52 - 36 * q^58 + 26 * q^64 - 32 * q^67 - 6 * q^70 + 16 * q^73 + 64 * q^76 + 40 * q^82 + 22 * q^88 + 24 * q^91 + 72 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.35760	+	0.396143i	0.959966	+	0.280116i
$2$	1.35760	+	0.396143i	0.959966	+	0.280116i
$3$		0			0
$3$		0			0
$4$	1.68614	+	1.07561i	0.843070	+	0.537803i
$5$	−0.505408			−0.226025			−0.113013	−	0.993594i	$-0.536050\pi$
$5$	−0.505408			−0.226025			−0.113013	+	0.993594i	$0.536050\pi$
$6$		0			0
$7$			3.42703i			1.29530i	0.761939	+	0.647649i	$0.224247\pi$
$7$			3.42703i			1.29530i	−0.761939	+	0.647649i	$0.775753\pi$
$8$	1.86301	+	2.12819i	0.658672	+	0.752430i
$9$		0			0
$10$	−0.686141	−	0.200214i	−0.216977	−	0.0633133i
$11$		−	3.31662i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$11$		−	3.31662i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$12$		0			0
$13$		−	2.55164i		−	0.707698i	−0.935303	−	0.353849i	$-0.884873\pi$
$13$		−	2.55164i		−	0.707698i	0.935303	−	0.353849i	$-0.115127\pi$
$14$	−1.35760	+	4.65253i	−0.362833	+	1.24344i
$15$		0			0
$16$	1.68614	+	3.62725i	0.421535	+	0.906812i
$17$		−	5.04868i		−	1.22448i	−0.790671	−	0.612242i	$-0.790268\pi$
$17$		−	5.04868i		−	1.22448i	0.790671	−	0.612242i	$-0.209732\pi$
$18$		0			0
$19$	4.74456			1.08848			0.544239	−	0.838930i	$-0.316819\pi$
$19$	4.74456			1.08848			0.544239	+	0.838930i	$0.316819\pi$
$20$	−0.852189	−	0.543620i	−0.190555	−	0.121557i
$21$		0			0
$22$	1.31386	−	4.50264i	0.280116	−	0.959966i
$23$	−6.44121			−1.34308			−0.671542	−	0.740966i	$-0.734368\pi$
$23$	−6.44121			−1.34308			−0.671542	+	0.740966i	$0.734368\pi$
$24$		0			0
$25$	−4.74456			−0.948913
$26$	1.01082	−	3.46410i	0.198237	−	0.679366i
$27$		0			0
$28$	−3.68614	+	5.77846i	−0.696615	+	1.09203i
$29$	−5.43039			−1.00840			−0.504199	−	0.863588i	$-0.668212\pi$
$29$	−5.43039			−1.00840			−0.504199	+	0.863588i	$0.668212\pi$
$30$		0			0
$31$			5.97868i			1.07380i	0.843645	+	0.536901i	$0.180405\pi$
$31$			5.97868i			1.07380i	−0.843645	+	0.536901i	$0.819595\pi$
$32$	0.852189	+	5.59230i	0.150647	+	0.988588i
$33$		0			0
$34$	2.00000	−	6.85407i	0.342997	−	1.17546i
$35$		−	1.73205i		−	0.292770i
$36$		0			0
$37$		−	11.1565i		−	1.83412i	−0.398753	−	0.917058i	$-0.630557\pi$
$37$		−	11.1565i		−	1.83412i	0.398753	−	0.917058i	$-0.369443\pi$
$38$	6.44121	+	1.87953i	1.04490	+	0.304900i
$39$		0			0
$40$	−0.941578	−	1.07561i	−0.148877	−	0.170068i
$41$			1.87953i			0.293533i	0.989171	+	0.146766i	$0.0468866\pi$
$41$			1.87953i			0.293533i	−0.989171	+	0.146766i	$0.953113\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	3.56738	−	5.59230i	0.537803	−	0.843070i
$45$		0			0
$46$	−8.74456	−	2.55164i	−1.28932	−	0.376219i
$47$	10.8608			1.58421			0.792104	−	0.610387i	$-0.208986\pi$
$47$	10.8608			1.58421			0.792104	+	0.610387i	$0.208986\pi$
$48$		0			0
$49$	−4.74456			−0.677795
$50$	−6.44121	−	1.87953i	−0.910924	−	0.265805i
$51$		0			0
$52$	2.74456	−	4.30243i	0.380602	−	0.596639i
$53$	5.93580			0.815344			0.407672	−	0.913128i	$-0.366341\pi$
$53$	5.93580			0.815344			0.407672	+	0.913128i	$0.366341\pi$
$54$		0			0
$55$			1.67625i			0.226025i
$56$	−7.29339	+	6.38458i	−0.974621	+	0.853176i
$57$		0			0
$58$	−7.37228	−	2.15121i	−0.968028	−	0.282468i
$59$			6.63325i			0.863576i	0.901975	+	0.431788i	$0.142117\pi$
$59$			6.63325i			0.863576i	−0.901975	+	0.431788i	$0.857883\pi$
$60$		0			0
$61$		−	5.10328i		−	0.653408i	−0.945127	−	0.326704i	$-0.894062\pi$
$61$		−	5.10328i		−	0.653408i	0.945127	−	0.326704i	$-0.105938\pi$
$62$	−2.36841	+	8.11663i	−0.300789	+	1.03081i
$63$		0			0
$64$	−1.05842	+	7.92967i	−0.132303	+	0.991209i
$65$			1.28962i			0.159958i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	5.43039	−	8.51278i	0.658531	−	1.03233i
$69$		0			0
$70$	0.686141	−	2.35143i	0.0820095	−	0.281049i
$71$	−4.41957			−0.524507			−0.262253	−	0.964999i	$-0.584466\pi$
$71$	−4.41957			−0.524507			−0.262253	+	0.964999i	$0.584466\pi$
$72$		0			0
$73$	7.74456			0.906432			0.453216	−	0.891401i	$-0.350277\pi$
$73$	7.74456			0.906432			0.453216	+	0.891401i	$0.350277\pi$
$74$	4.41957	−	15.1460i	0.513765	−	1.76069i
$75$		0			0
$76$	8.00000	+	5.10328i	0.917663	+	0.585387i
$77$	11.3662			1.29530
$78$		0			0
$79$			4.30243i			0.484061i	0.970269	+	0.242030i	$0.0778134\pi$
$79$			4.30243i			0.484061i	−0.970269	+	0.242030i	$0.922187\pi$
$80$	−0.852189	−	1.83324i	−0.0952776	−	0.204963i
$81$		0			0
$82$	−0.744563	+	2.55164i	−0.0822232	+	0.281782i
$83$			3.61158i			0.396422i	0.980159	+	0.198211i	$0.0635132\pi$
$83$			3.61158i			0.396422i	−0.980159	+	0.198211i	$0.936487\pi$
$84$		0			0
$85$			2.55164i			0.276764i
$86$	−5.43039	−	1.58457i	−0.585574	−	0.170869i
$87$		0			0
$88$	7.05842	−	6.17889i	0.752430	−	0.658672i
$89$			17.0256i			1.80471i	0.430999	+	0.902353i	$0.358161\pi$
$89$			17.0256i			1.80471i	−0.430999	+	0.902353i	$0.641839\pi$
$90$		0			0
$91$	8.74456			0.916679
$92$	−10.8608	−	6.92820i	−1.13231	−	0.722315i
$93$		0			0
$94$	14.7446	+	4.30243i	1.52079	+	0.443761i
$95$	−2.39794			−0.246023
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−6.44121	−	1.87953i	−0.650660	−	0.189861i
$99$		0			0
$100$	−8.00000	−	5.10328i	−0.800000	−	0.510328i
$101$	−15.7858			−1.57074			−0.785371	−	0.619026i	$-0.787528\pi$
$101$	−15.7858			−1.57074			−0.785371	+	0.619026i	$0.787528\pi$
$102$		0			0
$103$		−	0.800857i		−	0.0789107i	−0.999221	−	0.0394554i	$-0.987438\pi$
$103$		−	0.800857i		−	0.0789107i	0.999221	−	0.0394554i	$-0.0125623\pi$
$104$	5.43039	−	4.75372i	0.532493	−	0.466141i
$105$		0			0
$106$	8.05842	+	2.35143i	0.782703	+	0.228391i
$107$			4.90120i			0.473817i	0.971532	+	0.236908i	$0.0761341\pi$
$107$			4.90120i			0.473817i	−0.971532	+	0.236908i	$0.923866\pi$
$108$		0			0
$109$			11.1565i			1.06860i	0.845295	+	0.534299i	$0.179424\pi$
$109$			11.1565i			1.06860i	−0.845295	+	0.534299i	$0.820576\pi$
$110$	−0.664035	+	2.27567i	−0.0633133	+	0.216977i
$111$		0			0
$112$	−12.4307	+	5.77846i	−1.17459	+	0.546013i
$113$		−	11.9769i		−	1.12669i	−0.826222	−	0.563345i	$-0.809514\pi$
$113$		−	11.9769i		−	1.12669i	0.826222	−	0.563345i	$-0.190486\pi$
$114$		0			0
$115$	3.25544			0.303571
$116$	−9.15640	−	5.84096i	−0.850150	−	0.542320i
$117$		0			0
$118$	−2.62772	+	9.00528i	−0.241901	+	0.829003i
$119$	17.3020			1.58607
$120$		0			0
$121$		0			0
$122$	2.02163	−	6.92820i	0.183030	−	0.627250i
$123$		0			0
$124$	−6.43070	+	10.0809i	−0.577494	+	0.905290i
$125$	4.92498			0.440504
$126$		0			0
$127$		−	10.2811i		−	0.912300i	−0.889903	−	0.456150i	$-0.849228\pi$
$127$		−	10.2811i		−	0.912300i	0.889903	−	0.456150i	$-0.150772\pi$
$128$	−4.57820	+	10.3460i	−0.404660	+	0.914467i
$129$		0			0
$130$	−0.510875	+	1.75079i	−0.0448067	+	0.153554i
$131$		−	2.02700i		−	0.177100i	−0.996072	−	0.0885501i	$-0.971777\pi$
$131$		−	2.02700i		−	0.177100i	0.996072	−	0.0885501i	$-0.0282233\pi$
$132$		0			0
$133$			16.2598i			1.40990i
$134$	−5.43039	−	1.58457i	−0.469114	−	0.136886i
$135$		0			0
$136$	10.7446	−	9.40571i	0.921339	−	0.806533i
$137$			17.0256i			1.45459i	0.686324	+	0.727296i	$0.259223\pi$
$137$			17.0256i			1.45459i	−0.686324	+	0.727296i	$0.740777\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	1.86301	−	2.92048i	0.157453	−	0.246826i
$141$		0			0
$142$	−6.00000	−	1.75079i	−0.503509	−	0.146923i
$143$	−8.46284			−0.707698
$144$		0			0
$145$	2.74456			0.227924
$146$	10.5140	+	3.06796i	0.870145	+	0.253906i
$147$		0			0
$148$	12.0000	−	18.8114i	0.986394	−	1.54629i
$149$	18.8182			1.54165			0.770824	−	0.637048i	$-0.219845\pi$
$149$	18.8182			1.54165			0.770824	+	0.637048i	$0.219845\pi$
$150$		0			0
$151$		−	7.72946i		−	0.629015i	−0.949255	−	0.314507i	$-0.898161\pi$
$151$		−	7.72946i		−	0.629015i	0.949255	−	0.314507i	$-0.101839\pi$
$152$	8.83915	+	10.0974i	0.716949	+	0.819003i
$153$		0			0
$154$	15.4307	+	4.50264i	1.24344	+	0.362833i
$155$		−	3.02167i		−	0.242706i
$156$		0			0
$157$			5.10328i			0.407286i	0.979045	+	0.203643i	$0.0652782\pi$
$157$			5.10328i			0.407286i	−0.979045	+	0.203643i	$0.934722\pi$
$158$	−1.70438	+	5.84096i	−0.135593	+	0.464682i
$159$		0			0
$160$	−0.430703	−	2.82639i	−0.0340501	−	0.223446i
$161$		−	22.0742i		−	1.73969i
$162$		0			0
$163$	−18.2337			−1.42817			−0.714086	−	0.700058i	$-0.753158\pi$
$163$	−18.2337			−1.42817			−0.714086	+	0.700058i	$0.753158\pi$
$164$	−2.02163	+	3.16915i	−0.157863	+	0.247469i
$165$		0			0
$166$	−1.43070	+	4.90307i	−0.111044	+	0.380552i
$167$	−2.02163			−0.156439			−0.0782193	−	0.996936i	$-0.524923\pi$
$167$	−2.02163			−0.156439			−0.0782193	+	0.996936i	$0.524923\pi$
$168$		0			0
$169$	6.48913			0.499163
$170$	−1.01082	+	3.46410i	−0.0775261	+	0.265684i
$171$		0			0
$172$	−6.74456	−	4.30243i	−0.514268	−	0.328057i
$173$	−11.3662			−0.864155			−0.432078	−	0.901836i	$-0.642219\pi$
$173$	−11.3662			−0.864155			−0.432078	+	0.901836i	$0.642219\pi$
$174$		0			0
$175$		−	16.2598i		−	1.22912i
$176$	12.0302	−	5.59230i	0.906812	−	0.421535i
$177$		0			0
$178$	−6.74456	+	23.1138i	−0.505526	+	1.73246i
$179$			11.8294i			0.884171i	0.896973	+	0.442086i	$0.145761\pi$
$179$			11.8294i			0.884171i	−0.896973	+	0.442086i	$0.854239\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	11.8716	+	3.46410i	0.879981	+	0.256776i
$183$		0			0
$184$	−12.0000	−	13.7081i	−0.884652	−	1.01058i
$185$			5.63858i			0.414557i
$186$		0			0
$187$	−16.7446			−1.22448
$188$	18.3128	+	11.6819i	1.33560	+	0.851992i
$189$		0			0
$190$	−3.25544	−	0.949929i	−0.236174	−	0.0689151i
$191$	−8.46284			−0.612349			−0.306175	−	0.951975i	$-0.599049\pi$
$191$	−8.46284			−0.612349			−0.306175	+	0.951975i	$0.599049\pi$
$192$		0			0
$193$	13.2337			0.952582			0.476291	−	0.879288i	$-0.341981\pi$
$193$	13.2337			0.952582			0.476291	+	0.879288i	$0.341981\pi$
$194$	−1.35760	−	0.396143i	−0.0974698	−	0.0284414i
$195$		0			0
$196$	−8.00000	−	5.10328i	−0.571429	−	0.364520i
$197$	−13.3878			−0.953843			−0.476921	−	0.878946i	$-0.658247\pi$
$197$	−13.3878			−0.953843			−0.476921	+	0.878946i	$0.658247\pi$
$198$		0			0
$199$		−	6.77953i		−	0.480588i	−0.970700	−	0.240294i	$-0.922756\pi$
$199$		−	6.77953i		−	0.480588i	0.970700	−	0.240294i	$-0.0772439\pi$
$200$	−8.83915	−	10.0974i	−0.625022	−	0.713991i
$201$		0			0
$202$	−21.4307	−	6.25343i	−1.50786	−	0.439990i
$203$		−	18.6101i		−	1.30617i
$204$		0			0
$205$		−	0.949929i		−	0.0663459i
$206$	0.317254	−	1.08724i	0.0221041	−	0.0757516i
$207$		0			0
$208$	9.25544	−	4.30243i	0.641749	−	0.298320i
$209$		−	15.7359i		−	1.08848i
$210$		0			0
$211$	−12.7446			−0.877372			−0.438686	−	0.898640i	$-0.644556\pi$
$211$	−12.7446			−0.877372			−0.438686	+	0.898640i	$0.644556\pi$
$212$	10.0086	+	6.38458i	0.687393	+	0.438495i
$213$		0			0
$214$	−1.94158	+	6.65385i	−0.132724	+	0.454848i
$215$	2.02163			0.137874
$216$		0			0
$217$	−20.4891			−1.39089
$218$	−4.41957	+	15.1460i	−0.299331	+	1.02582i
$219$		0			0
$220$	−1.80298	+	2.82639i	−0.121557	+	0.190555i
$221$	−12.8824			−0.866565
$222$		0			0
$223$		−	18.0106i		−	1.20608i	−0.797712	−	0.603038i	$-0.793957\pi$
$223$		−	18.0106i		−	1.20608i	0.797712	−	0.603038i	$-0.206043\pi$
$224$	−19.1650	+	2.92048i	−1.28051	+	0.195133i
$225$		0			0
$226$	4.74456	−	16.2598i	0.315604	−	1.08158i
$227$		−	23.6588i		−	1.57029i	−0.619312	−	0.785145i	$-0.712588\pi$
$227$		−	23.6588i		−	1.57029i	0.619312	−	0.785145i	$-0.287412\pi$
$228$		0			0
$229$			8.60485i			0.568625i	0.958732	+	0.284312i	$0.0917653\pi$
$229$			8.60485i			0.568625i	−0.958732	+	0.284312i	$0.908235\pi$
$230$	4.41957	+	1.28962i	0.291418	+	0.0850350i
$231$		0			0
$232$	−10.1168	−	11.5569i	−0.664203	−	0.758749i
$233$			0.589907i			0.0386461i	0.999813	+	0.0193231i	$0.00615110\pi$
$233$			0.589907i			0.0386461i	−0.999813	+	0.0193231i	$0.993849\pi$
$234$		0			0
$235$	−5.48913			−0.358071
$236$	−7.13477	+	11.1846i	−0.464434	+	0.728055i
$237$		0			0
$238$	23.4891	+	6.85407i	1.52257	+	0.444283i
$239$	−15.2804			−0.988404			−0.494202	−	0.869347i	$-0.664540\pi$
$239$	−15.2804			−0.988404			−0.494202	+	0.869347i	$0.664540\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$		0			0
$243$		0			0
$244$	5.48913	−	8.60485i	0.351405	−	0.550869i
$245$	2.39794			0.153199
$246$		0			0
$247$		−	12.1064i		−	0.770313i
$248$	−12.7238	+	11.1383i	−0.807961	+	0.707283i
$249$		0			0
$250$	6.68614	+	1.95100i	0.422869	+	0.123392i
$251$		−	9.80240i		−	0.618722i	−0.950945	−	0.309361i	$-0.899885\pi$
$251$		−	9.80240i		−	0.618722i	0.950945	−	0.309361i	$-0.100115\pi$
$252$		0			0
$253$			21.3631i			1.34308i
$254$	4.07279	−	13.9576i	0.255550	−	0.875777i
$255$		0			0
$256$	−10.3139	+	12.2321i	−0.644616	+	0.764506i
$257$		−	18.9051i		−	1.17927i	−0.807671	−	0.589633i	$-0.799272\pi$
$257$		−	18.9051i		−	1.17927i	0.807671	−	0.589633i	$-0.200728\pi$
$258$		0			0
$259$	38.2337			2.37573
$260$	−1.38712	+	2.17448i	−0.0860258	+	0.134856i
$261$		0			0
$262$	0.802985	−	2.75186i	0.0496086	−	0.170010i
$263$	6.44121			0.397182			0.198591	−	0.980082i	$-0.436364\pi$
$263$	6.44121			0.397182			0.198591	+	0.980082i	$0.436364\pi$
$264$		0			0
$265$	−3.00000			−0.184289
$266$	−6.44121	+	22.0742i	−0.394936	+	1.35346i
$267$		0			0
$268$	−6.74456	−	4.30243i	−0.411990	−	0.262813i
$269$	7.45202			0.454358			0.227179	−	0.973853i	$-0.427050\pi$
$269$	7.45202			0.454358			0.227179	+	0.973853i	$0.427050\pi$
$270$		0			0
$271$			23.1884i			1.40859i	0.709905	+	0.704297i	$0.248738\pi$
$271$			23.1884i			1.40859i	−0.709905	+	0.704297i	$0.751262\pi$
$272$	18.3128	−	8.51278i	1.11038	−	0.516163i
$273$		0			0
$274$	−6.74456	+	23.1138i	−0.407454	+	1.39636i
$275$			15.7359i			0.948913i
$276$		0			0
$277$		−	5.10328i		−	0.306627i	−0.988178	−	0.153313i	$-0.951006\pi$
$277$		−	5.10328i		−	0.306627i	0.988178	−	0.153313i	$-0.0489944\pi$
$278$	10.8608	+	3.16915i	0.651386	+	0.190073i
$279$		0			0
$280$	3.68614	−	3.22682i	0.220289	−	0.192839i
$281$			8.80773i			0.525425i	0.964874	+	0.262713i	$0.0846171\pi$
$281$			8.80773i			0.525425i	−0.964874	+	0.262713i	$0.915383\pi$
$282$		0			0
$283$	11.2554			0.669066			0.334533	−	0.942384i	$-0.391421\pi$
$283$	11.2554			0.669066			0.334533	+	0.942384i	$0.391421\pi$
$284$	−7.45202	−	4.75372i	−0.442196	−	0.282082i
$285$		0			0
$286$	−11.4891	−	3.35250i	−0.679366	−	0.198237i
$287$	−6.44121			−0.380212
$288$		0			0
$289$	−8.48913			−0.499360
$290$	3.72601	+	1.08724i	0.218799	+	0.0638450i
$291$		0			0
$292$	13.0584	+	8.33010i	0.764186	+	0.487482i
$293$	−9.47365			−0.553457			−0.276728	−	0.960948i	$-0.589250\pi$
$293$	−9.47365			−0.553457			−0.276728	+	0.960948i	$0.589250\pi$
$294$		0			0
$295$		−	3.35250i		−	0.195190i
$296$	23.7432	−	20.7846i	1.38004	−	1.20808i
$297$		0			0
$298$	25.5475	+	7.45471i	1.47993	+	0.431840i
$299$			16.4356i			0.950498i
$300$		0			0
$301$		−	13.7081i		−	0.790124i
$302$	3.06198	−	10.4935i	0.176197	−	0.603833i
$303$		0			0
$304$	8.00000	+	17.2097i	0.458831	+	0.987044i
$305$			2.57924i			0.147687i
$306$		0			0
$307$	−7.25544			−0.414090			−0.207045	−	0.978331i	$-0.566385\pi$
$307$	−7.25544			−0.414090			−0.207045	+	0.978331i	$0.566385\pi$
$308$	19.1650	+	12.2255i	1.09203	+	0.696615i
$309$		0			0
$310$	1.19702	−	4.10221i	0.0679859	−	0.232990i
$311$	2.39794			0.135975			0.0679874	−	0.997686i	$-0.478342\pi$
$311$	2.39794			0.135975			0.0679874	+	0.997686i	$0.478342\pi$
$312$		0			0
$313$	25.2337			1.42629			0.713146	−	0.701015i	$-0.247270\pi$
$313$	25.2337			1.42629			0.713146	+	0.701015i	$0.247270\pi$
$314$	−2.02163	+	6.92820i	−0.114087	+	0.390981i
$315$		0			0
$316$	−4.62772	+	7.25450i	−0.260330	+	0.408097i
$317$	7.95743			0.446934			0.223467	−	0.974712i	$-0.428263\pi$
$317$	7.95743			0.446934			0.223467	+	0.974712i	$0.428263\pi$
$318$		0			0
$319$			18.0106i			1.00840i
$320$	0.534935	−	4.00772i	0.0299038	−	0.224038i
$321$		0			0
$322$	8.74456	−	29.9679i	0.487315	−	1.67005i
$323$		−	23.9538i		−	1.33282i
$324$		0			0
$325$			12.1064i			0.671544i
$326$	−24.7540	−	7.22316i	−1.37100	−	0.400054i
$327$		0			0
$328$	−4.00000	+	3.50157i	−0.220863	+	0.193342i
$329$			37.2203i			2.05202i
$330$		0			0
$331$	−10.5109			−0.577730			−0.288865	−	0.957370i	$-0.593278\pi$
$331$	−10.5109			−0.577730			−0.288865	+	0.957370i	$0.593278\pi$
$332$	−3.88464	+	6.08963i	−0.213197	+	0.334212i
$333$		0			0
$334$	−2.74456	−	0.800857i	−0.150176	−	0.0438209i
$335$	2.02163			0.110454
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	8.80962	+	2.57062i	0.479180	+	0.139824i
$339$		0			0
$340$	−2.74456	+	4.30243i	−0.148845	+	0.233332i
$341$	19.8290			1.07380
$342$		0			0
$343$			7.72946i			0.417352i
$344$	−7.45202	−	8.51278i	−0.401786	−	0.458978i
$345$		0			0
$346$	−15.4307	−	4.50264i	−0.829560	−	0.242063i
$347$			26.9754i			1.44812i	0.689739	+	0.724058i	$0.257725\pi$
$347$			26.9754i			1.44812i	−0.689739	+	0.724058i	$0.742275\pi$
$348$		0			0
$349$		−	16.2598i		−	0.870366i	−0.900342	−	0.435183i	$-0.856684\pi$
$349$		−	16.2598i		−	0.870366i	0.900342	−	0.435183i	$-0.143316\pi$
$350$	6.44121	−	22.0742i	0.344297	−	1.17992i
$351$		0			0
$352$	18.5475	−	2.82639i	0.988588	−	0.150647i
$353$		−	28.4125i		−	1.51225i	−0.654429	−	0.756123i	$-0.727091\pi$
$353$		−	28.4125i		−	1.51225i	0.654429	−	0.756123i	$-0.272909\pi$
$354$		0			0
$355$	2.23369			0.118552
$356$	−18.3128	+	28.7075i	−0.970576	+	1.52149i
$357$		0			0
$358$	−4.68614	+	16.0596i	−0.247670	+	0.848774i
$359$	23.7432			1.25312			0.626559	−	0.779374i	$-0.284463\pi$
$359$	23.7432			1.25312			0.626559	+	0.779374i	$0.284463\pi$
$360$		0			0
$361$	3.51087			0.184783
$362$		0			0
$363$		0			0
$364$	14.7446	+	9.40571i	0.772825	+	0.492993i
$365$	−3.91416			−0.204877
$366$		0			0
$367$			11.0820i			0.578474i	0.957258	+	0.289237i	$0.0934015\pi$
$367$			11.0820i			0.578474i	−0.957258	+	0.289237i	$0.906599\pi$
$368$	−10.8608	−	23.3639i	−0.566157	−	1.21792i
$369$		0			0
$370$	−2.23369	+	7.65492i	−0.116124	+	0.397961i
$371$			20.3422i			1.05611i
$372$		0			0
$373$		−	2.55164i		−	0.132119i	−0.997816	−	0.0660595i	$-0.978957\pi$
$373$		−	2.55164i		−	0.132119i	0.997816	−	0.0660595i	$-0.0210427\pi$
$374$	−22.7324	−	6.63325i	−1.17546	−	0.342997i
$375$		0			0
$376$	20.2337	+	23.1138i	1.04347	+	1.19201i
$377$			13.8564i			0.713641i
$378$		0			0
$379$	−9.48913			−0.487424			−0.243712	−	0.969848i	$-0.578365\pi$
$379$	−9.48913			−0.487424			−0.243712	+	0.969848i	$0.578365\pi$
$380$	−4.04326	−	2.57924i	−0.207415	−	0.132312i
$381$		0			0
$382$	−11.4891	−	3.35250i	−0.587835	−	0.171529i
$383$	26.1411			1.33575			0.667875	−	0.744274i	$-0.267204\pi$
$383$	26.1411			1.33575			0.667875	+	0.744274i	$0.267204\pi$
$384$		0			0
$385$	−5.74456			−0.292770
$386$	17.9660	+	5.24244i	0.914446	+	0.266833i
$387$		0			0
$388$	−1.68614	−	1.07561i	−0.0856008	−	0.0546057i
$389$	22.8615			1.15912			0.579561	−	0.814929i	$-0.303224\pi$
$389$	22.8615			1.15912			0.579561	+	0.814929i	$0.303224\pi$
$390$		0			0
$391$			32.5196i			1.64458i
$392$	−8.83915	−	10.0974i	−0.446444	−	0.509993i
$393$		0			0
$394$	−18.1753	−	5.30350i	−0.915657	−	0.267186i
$395$		−	2.17448i		−	0.109410i
$396$		0			0
$397$		−	29.9679i		−	1.50405i	−0.659137	−	0.752023i	$-0.729078\pi$
$397$		−	29.9679i		−	1.50405i	0.659137	−	0.752023i	$-0.270922\pi$
$398$	2.68567	−	9.20387i	0.134620	−	0.461349i
$399$		0			0
$400$	−8.00000	−	17.2097i	−0.400000	−	0.860485i
$401$		−	3.75906i		−	0.187718i	−0.995585	−	0.0938591i	$-0.970080\pi$
$401$		−	3.75906i		−	0.187718i	0.995585	−	0.0938591i	$-0.0299203\pi$
$402$		0			0
$403$	15.2554			0.759927
$404$	−26.6170	−	16.9793i	−1.32425	−	0.844750i
$405$		0			0
$406$	7.37228	−	25.2651i	0.365880	−	1.25388i
$407$	−37.0019			−1.83412
$408$		0			0
$409$	11.0000			0.543915			0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000			0.543915			0.271957	+	0.962309i	$0.412329\pi$
$410$	0.376308	−	1.28962i	0.0185845	−	0.0636898i
$411$		0			0
$412$	0.861407	−	1.35036i	0.0424385	−	0.0665273i
$413$	−22.7324			−1.11859
$414$		0			0
$415$		−	1.82532i		−	0.0896015i
$416$	14.2695	−	2.17448i	0.699622	−	0.106613i
$417$		0			0
$418$	6.23369	−	21.3631i	0.304900	−	1.04490i
$419$		−	7.22316i		−	0.352874i	−0.984312	−	0.176437i	$-0.943543\pi$
$419$		−	7.22316i		−	0.352874i	0.984312	−	0.176437i	$-0.0564572\pi$
$420$		0			0
$421$		−	27.4163i		−	1.33619i	−0.744077	−	0.668094i	$-0.767111\pi$
$421$		−	27.4163i		−	1.33619i	0.744077	−	0.668094i	$-0.232889\pi$
$422$	−17.3020	−	5.04868i	−0.842247	−	0.245766i
$423$		0			0
$424$	11.0584	+	12.6325i	0.537044	+	0.613490i
$425$			23.9538i			1.16193i
$426$		0			0
$427$	17.4891			0.846358
$428$	−5.27176	+	8.26411i	−0.254820	+	0.399461i
$429$		0			0
$430$	2.74456	+	0.800857i	0.132355	+	0.0386207i
$431$	14.9040			0.717902			0.358951	−	0.933356i	$-0.383134\pi$
$431$	14.9040			0.717902			0.358951	+	0.933356i	$0.383134\pi$
$432$		0			0
$433$	−18.4891			−0.888531			−0.444265	−	0.895895i	$-0.646535\pi$
$433$	−18.4891			−0.888531			−0.444265	+	0.895895i	$0.646535\pi$
$434$	−27.8160	−	8.11663i	−1.33521	−	0.389611i
$435$		0			0
$436$	−12.0000	+	18.8114i	−0.574696	+	0.900904i
$437$	−30.5607			−1.46192
$438$		0			0
$439$			18.7369i			0.894263i	0.894468	+	0.447131i	$0.147554\pi$
$439$			18.7369i			0.894263i	−0.894468	+	0.447131i	$0.852446\pi$
$440$	−3.56738	+	3.12286i	−0.170068	+	0.148877i
$441$		0			0
$442$	−17.4891	−	5.10328i	−0.831873	−	0.242738i
$443$			6.63325i			0.315155i	0.987507	+	0.157578i	$0.0503684\pi$
$443$			6.63325i			0.315155i	−0.987507	+	0.157578i	$0.949632\pi$
$444$		0			0
$445$		−	8.60485i		−	0.407909i
$446$	7.13477	−	24.4511i	0.337841	−	1.15779i
$447$		0			0
$448$	−27.1753	−	3.62725i	−1.28391	−	0.171371i
$449$			4.45877i			0.210422i	0.994450	+	0.105211i	$0.0335518\pi$
$449$			4.45877i			0.210422i	−0.994450	+	0.105211i	$0.966448\pi$
$450$		0			0
$451$	6.23369			0.293533
$452$	12.8824	−	20.1947i	0.605938	−	0.949879i
$453$		0			0
$454$	9.37228	−	32.1191i	0.439863	−	1.50743i
$455$	−4.41957			−0.207193
$456$		0			0
$457$	−41.4674			−1.93976			−0.969881	−	0.243579i	$-0.921678\pi$
$457$	−41.4674			−1.93976			−0.969881	+	0.243579i	$0.921678\pi$
$458$	−3.40876	+	11.6819i	−0.159281	+	0.545861i
$459$		0			0
$460$	5.48913	+	3.50157i	0.255932	+	0.163262i
$461$	34.4749			1.60565			0.802827	−	0.596212i	$-0.203328\pi$
$461$	34.4749			1.60565			0.802827	+	0.596212i	$0.203328\pi$
$462$		0			0
$463$		−	31.6442i		−	1.47063i	−0.677726	−	0.735314i	$-0.737034\pi$
$463$		−	31.6442i		−	1.47063i	0.677726	−	0.735314i	$-0.262966\pi$
$464$	−9.15640	−	19.6974i	−0.425075	−	0.914427i
$465$		0			0
$466$	−0.233688	+	0.800857i	−0.0108254	+	0.0370990i
$467$			31.3244i			1.44952i	0.689001	+	0.724760i	$0.258049\pi$
$467$			31.3244i			1.44952i	−0.689001	+	0.724760i	$0.741951\pi$
$468$		0			0
$469$		−	13.7081i		−	0.632983i
$470$	−7.45202	−	2.17448i	−0.343736	−	0.100301i
$471$		0			0
$472$	−14.1168	+	12.3578i	−0.649780	+	0.568813i
$473$			13.2665i			0.609994i
$474$		0			0
$475$	−22.5109			−1.03287
$476$	29.1736	+	18.6101i	1.33717	+	0.852994i
$477$		0			0
$478$	−20.7446	−	6.05321i	−0.948834	−	0.276867i
$479$	2.02163			0.0923707			0.0461854	−	0.998933i	$-0.485294\pi$
$479$	2.02163			0.0923707			0.0461854	+	0.998933i	$0.485294\pi$
$480$		0			0
$481$	−28.4674			−1.29800
$482$	2.71519	+	0.792287i	0.123674	+	0.0360877i
$483$		0			0
$484$		0			0
$485$	0.505408			0.0229494
$486$		0			0
$487$			9.40571i			0.426213i	0.977029	+	0.213107i	$0.0683582\pi$
$487$			9.40571i			0.426213i	−0.977029	+	0.213107i	$0.931642\pi$
$488$	10.8608	−	9.50744i	0.491644	−	0.430382i
$489$		0			0
$490$	3.25544	+	0.949929i	0.147066	+	0.0429134i
$491$		−	27.9701i		−	1.26227i	−0.775672	−	0.631136i	$-0.782589\pi$
$491$		−	27.9701i		−	1.26227i	0.775672	−	0.631136i	$-0.217411\pi$
$492$		0			0
$493$			27.4163i			1.23477i
$494$	4.79588	−	16.4356i	0.215777	−	0.739475i
$495$		0			0
$496$	−21.6861	+	10.0809i	−0.973736	+	0.452645i
$497$		−	15.1460i		−	0.679392i
$498$		0			0
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$	8.30421	+	5.29734i	0.371376	+	0.236904i
$501$		0			0
$502$	3.88316	−	13.3077i	0.173314	−	0.593952i
$503$	−19.3236			−0.861597			−0.430799	−	0.902448i	$-0.641768\pi$
$503$	−19.3236			−0.861597			−0.430799	+	0.902448i	$0.641768\pi$
$504$		0			0
$505$	7.97825			0.355027
$506$	−8.46284	+	29.0024i	−0.376219	+	1.28932i
$507$		0			0
$508$	11.0584	−	17.3354i	0.490638	−	0.769133i
$509$	23.2378			1.03000			0.514998	−	0.857191i	$-0.327793\pi$
$509$	23.2378			1.03000			0.514998	+	0.857191i	$0.327793\pi$
$510$		0			0
$511$			26.5409i			1.17410i
$512$	−18.8477	+	12.5205i	−0.832960	+	0.553333i
$513$		0			0
$514$	7.48913	−	25.6655i	0.330331	−	1.13206i
$515$			0.404759i			0.0178358i
$516$		0			0
$517$		−	36.0211i		−	1.58421i
$518$	51.9060	+	15.1460i	2.28062	+	0.665478i
$519$		0			0
$520$	−2.74456	+	2.40257i	−0.120357	+	0.105360i
$521$		−	5.04868i		−	0.221186i	−0.993866	−	0.110593i	$-0.964725\pi$
$521$		−	5.04868i		−	0.221186i	0.993866	−	0.110593i	$-0.0352751\pi$
$522$		0			0
$523$	34.2337			1.49693			0.748467	−	0.663172i	$-0.230790\pi$
$523$	34.2337			1.49693			0.748467	+	0.663172i	$0.230790\pi$
$524$	2.18026	−	3.41781i	0.0952451	−	0.149308i
$525$		0			0
$526$	8.74456	+	2.55164i	0.381281	+	0.111257i
$527$	30.1844			1.31485
$528$		0			0
$529$	18.4891			0.803875
$530$	−4.07279	−	1.18843i	−0.176911	−	0.0516221i
$531$		0			0
$532$	−17.4891	+	27.4163i	−0.758250	+	1.18865i
$533$	4.79588			0.207733
$534$		0			0
$535$		−	2.47711i		−	0.107095i
$536$	−7.45202	−	8.51278i	−0.321878	−	0.367696i
$537$		0			0
$538$	10.1168	+	2.95207i	0.436168	+	0.127273i
$539$			15.7359i			0.677795i
$540$		0			0
$541$		−	37.6228i		−	1.61753i	−0.588130	−	0.808766i	$-0.700136\pi$
$541$		−	37.6228i		−	1.61753i	0.588130	−	0.808766i	$-0.299864\pi$
$542$	−9.18593	+	31.4805i	−0.394569	+	1.35220i
$543$		0			0
$544$	28.2337	−	4.30243i	1.21051	−	0.184465i
$545$		−	5.63858i		−	0.241530i
$546$		0			0
$547$	5.76631			0.246550			0.123275	−	0.992373i	$-0.460660\pi$
$547$	5.76631			0.246550			0.123275	+	0.992373i	$0.460660\pi$
$548$	−18.3128	+	28.7075i	−0.782284	+	1.22632i
$549$		0			0
$550$	−6.23369	+	21.3631i	−0.265805	+	0.910924i
$551$	−25.7648			−1.09762
$552$		0			0
$553$	−14.7446			−0.627003
$554$	2.02163	−	6.92820i	0.0858909	−	0.294351i
$555$		0			0
$556$	13.4891	+	8.60485i	0.572066	+	0.364927i
$557$	−8.96825			−0.379997			−0.189998	−	0.981784i	$-0.560848\pi$
$557$	−8.96825			−0.379997			−0.189998	+	0.981784i	$0.560848\pi$
$558$		0			0
$559$			10.2066i			0.431692i
$560$	6.28258	−	2.92048i	0.265487	−	0.123413i
$561$		0			0
$562$	−3.48913	+	11.9574i	−0.147180	+	0.504390i
$563$		−	12.8241i		−	0.540470i	−0.962794	−	0.270235i	$-0.912899\pi$
$563$		−	12.8241i		−	0.540470i	0.962794	−	0.270235i	$-0.0871014\pi$
$564$		0			0
$565$			6.05321i			0.254661i
$566$	15.2804	+	4.45877i	0.642281	+	0.187416i
$567$		0			0
$568$	−8.23369	−	9.40571i	−0.345478	−	0.394655i
$569$			7.51811i			0.315176i	0.987505	+	0.157588i	$0.0503717\pi$
$569$			7.51811i			0.315176i	−0.987505	+	0.157588i	$0.949628\pi$
$570$		0			0
$571$	34.2337			1.43264			0.716318	−	0.697774i	$-0.245826\pi$
$571$	34.2337			1.43264			0.716318	+	0.697774i	$0.245826\pi$
$572$	−14.2695	−	9.10268i	−0.596639	−	0.380602i
$573$		0			0
$574$	−8.74456	−	2.55164i	−0.364991	−	0.106503i
$575$	30.5607			1.27447
$576$		0			0
$577$	36.9783			1.53942			0.769712	−	0.638391i	$-0.220400\pi$
$577$	36.9783			1.53942			0.769712	+	0.638391i	$0.220400\pi$
$578$	−11.5248	−	3.36291i	−0.479369	−	0.139879i
$579$		0			0
$580$	4.62772	+	2.95207i	0.192156	+	0.122578i
$581$	−12.3770			−0.513485
$582$		0			0
$583$		−	19.6868i		−	0.815344i
$584$	14.4282	+	16.4819i	0.597042	+	0.682027i
$585$		0			0
$586$	−12.8614	−	3.75293i	−0.531300	−	0.155032i
$587$		−	39.2473i		−	1.61991i	−0.586494	−	0.809954i	$-0.699492\pi$
$587$		−	39.2473i		−	1.61991i	0.586494	−	0.809954i	$-0.300508\pi$
$588$		0			0
$589$			28.3662i			1.16881i
$590$	1.32807	−	4.55134i	0.0546758	−	0.187376i
$591$		0			0
$592$	40.4674	−	18.8114i	1.66320	−	0.773145i
$593$		−	13.2665i		−	0.544790i	−0.962186	−	0.272395i	$-0.912184\pi$
$593$		−	13.2665i		−	0.544790i	0.962186	−	0.272395i	$-0.0878157\pi$
$594$		0			0
$595$	−8.74456			−0.358492
$596$	31.7301	+	20.2410i	1.29972	+	0.829103i
$597$		0			0
$598$	−6.51087	+	22.3130i	−0.266249	+	0.912446i
$599$	27.7865			1.13532			0.567662	−	0.823262i	$-0.307848\pi$
$599$	27.7865			1.13532			0.567662	+	0.823262i	$0.307848\pi$
$600$		0			0
$601$	−3.23369			−0.131905			−0.0659524	−	0.997823i	$-0.521009\pi$
$601$	−3.23369			−0.131905			−0.0659524	+	0.997823i	$0.521009\pi$
$602$	5.43039	−	18.6101i	0.221326	−	0.758492i
$603$		0			0
$604$	8.31386	−	13.0330i	0.338286	−	0.530304i
$605$		0			0
$606$		0			0
$607$			36.8220i			1.49456i	0.664510	+	0.747279i	$0.268640\pi$
$607$			36.8220i			1.49456i	−0.664510	+	0.747279i	$0.731360\pi$
$608$	4.04326	+	26.5330i	0.163976	+	1.07606i
$609$		0			0
$610$	−1.02175	+	3.50157i	−0.0413694	+	0.141774i
$611$		−	27.7128i		−	1.12114i
$612$		0			0
$613$			34.1213i			1.37815i	0.724692	+	0.689073i	$0.241982\pi$
$613$			34.1213i			1.37815i	−0.724692	+	0.689073i	$0.758018\pi$
$614$	−9.84996	−	2.87419i	−0.397512	−	0.115993i
$615$		0			0
$616$	21.1753	+	24.1895i	0.853176	+	0.974621i
$617$		−	28.4125i		−	1.14385i	−0.820308	−	0.571923i	$-0.806198\pi$
$617$		−	28.4125i		−	1.14385i	0.820308	−	0.571923i	$-0.193802\pi$
$618$		0			0
$619$	−42.2337			−1.69752			−0.848758	−	0.528782i	$-0.822649\pi$
$619$	−42.2337			−1.69752			−0.848758	+	0.528782i	$0.822649\pi$
$620$	3.25013	−	5.09496i	0.130528	−	0.204619i
$621$		0			0
$622$	3.25544	+	0.949929i	0.130531	+	0.0380887i
$623$	−58.3472			−2.33763
$624$		0			0
$625$	21.2337			0.849348
$626$	34.2572	+	9.99616i	1.36919	+	0.399527i
$627$		0			0
$628$	−5.48913	+	8.60485i	−0.219040	+	0.343371i
$629$	−56.3255			−2.24585
$630$		0			0
$631$		−	13.7827i		−	0.548680i	−0.961633	−	0.274340i	$-0.911541\pi$
$631$		−	13.7827i		−	0.548680i	0.961633	−	0.274340i	$-0.0884593\pi$
$632$	−9.15640	+	8.01544i	−0.364222	+	0.318837i
$633$		0			0
$634$	10.8030	+	3.15228i	0.429041	+	0.125193i
$635$			5.19615i			0.206203i
$636$		0			0
$637$			12.1064i			0.479674i
$638$	−7.13477	+	24.4511i	−0.282468	+	0.968028i
$639$		0			0
$640$	2.31386	−	5.22896i	0.0914633	−	0.206693i
$641$			1.87953i			0.0742369i	0.999311	+	0.0371184i	$0.0118179\pi$
$641$			1.87953i			0.0742369i	−0.999311	+	0.0371184i	$0.988182\pi$
$642$		0			0
$643$	−44.4674			−1.75362			−0.876811	−	0.480835i	$-0.840334\pi$
$643$	−44.4674			−1.75362			−0.876811	+	0.480835i	$0.840334\pi$
$644$	23.7432	−	37.2203i	0.935613	−	1.46668i
$645$		0			0
$646$	9.48913	−	32.5196i	0.373345	−	1.27946i
$647$	−29.8081			−1.17188			−0.585938	−	0.810356i	$-0.699274\pi$
$647$	−29.8081			−1.17188			−0.585938	+	0.810356i	$0.699274\pi$
$648$		0			0
$649$	22.0000			0.863576
$650$	−4.79588	+	16.4356i	−0.188110	+	0.644659i
$651$		0			0
$652$	−30.7446	−	19.6123i	−1.20405	−	0.768076i
$653$	−41.9269			−1.64073			−0.820363	−	0.571843i	$-0.806229\pi$
$653$	−41.9269			−1.64073			−0.820363	+	0.571843i	$0.806229\pi$
$654$		0			0
$655$			1.02446i			0.0400291i
$656$	−6.81751	+	3.16915i	−0.266179	+	0.123734i
$657$		0			0
$658$	−14.7446	+	50.5301i	−0.574803	+	1.96987i
$659$			39.5422i			1.54035i	0.637835	+	0.770173i	$0.279830\pi$
$659$			39.5422i			1.54035i	−0.637835	+	0.770173i	$0.720170\pi$
$660$		0			0
$661$			16.2598i			0.632432i	0.948687	+	0.316216i	$0.102412\pi$
$661$			16.2598i			0.632432i	−0.948687	+	0.316216i	$0.897588\pi$
$662$	−14.2695	−	4.16381i	−0.554601	−	0.161831i
$663$		0			0
$664$	−7.68614	+	6.72839i	−0.298280	+	0.261112i
$665$		−	8.21782i		−	0.318674i
$666$		0			0
$667$	34.9783			1.35436
$668$	−3.40876	−	2.17448i	−0.131889	−	0.0841332i
$669$		0			0
$670$	2.74456	+	0.800857i	0.106032	+	0.0309398i
$671$	−16.9257			−0.653408
$672$		0			0
$673$	−7.51087			−0.289523			−0.144761	−	0.989467i	$-0.546241\pi$
$673$	−7.51087			−0.289523			−0.144761	+	0.989467i	$0.546241\pi$
$674$	2.71519	+	0.792287i	0.104585	+	0.0305178i
$675$		0			0
$676$	10.9416	+	6.97975i	0.420830	+	0.268452i
$677$	42.0560			1.61634			0.808171	−	0.588947i	$-0.200457\pi$
$677$	42.0560			1.61634			0.808171	+	0.588947i	$0.200457\pi$
$678$		0			0
$679$		−	3.42703i		−	0.131517i
$680$	−5.43039	+	4.75372i	−0.208246	+	0.182297i
$681$		0			0
$682$	26.9198	+	7.85514i	1.03081	+	0.300789i
$683$		−	9.80240i		−	0.375078i	−0.982257	−	0.187539i	$-0.939949\pi$
$683$		−	9.80240i		−	0.375078i	0.982257	−	0.187539i	$-0.0600512\pi$
$684$		0			0
$685$		−	8.60485i		−	0.328775i
$686$	−3.06198	+	10.4935i	−0.116907	+	0.400643i
$687$		0			0
$688$	−6.74456	−	14.5090i	−0.257134	−	0.553150i
$689$		−	15.1460i		−	0.577018i
$690$		0			0
$691$	49.4891			1.88266			0.941328	−	0.337494i	$-0.109579\pi$
$691$	49.4891			1.88266			0.941328	+	0.337494i	$0.109579\pi$
$692$	−19.1650	−	12.2255i	−0.728544	−	0.464746i
$693$		0			0
$694$	−10.6861	+	36.6218i	−0.405640	+	1.39014i
$695$	−4.04326			−0.153370
$696$		0			0
$697$	9.48913			0.359426
$698$	6.44121	−	22.0742i	0.243803	−	0.835522i
$699$		0			0
$700$	17.4891	−	27.4163i	0.661027	−	1.03624i
$701$	10.3554			0.391117			0.195558	−	0.980692i	$-0.437348\pi$
$701$	10.3554			0.391117			0.195558	+	0.980692i	$0.437348\pi$
$702$		0			0
$703$		−	52.9327i		−	1.99639i
$704$	26.2998	+	3.51039i	0.991209	+	0.132303i
$705$		0			0
$706$	11.2554	−	38.5728i	0.423604	−	1.45171i
$707$		−	54.0983i		−	2.03458i
$708$		0			0
$709$		−	12.1064i		−	0.454666i	−0.973817	−	0.227333i	$-0.926999\pi$
$709$		−	12.1064i		−	0.454666i	0.973817	−	0.227333i	$-0.0730006\pi$
$710$	3.03245	+	0.884861i	0.113806	+	0.0332082i
$711$		0			0
$712$	−36.2337	+	31.7187i	−1.35791	+	1.18871i
$713$		−	38.5099i		−	1.44221i
$714$		0			0
$715$	4.27719			0.159958
$716$	−12.7238	+	19.9460i	−0.475510	+	0.745418i
$717$		0			0
$718$	32.2337	+	9.40571i	1.20295	+	0.351018i
$719$	−8.83915			−0.329645			−0.164822	−	0.986323i	$-0.552705\pi$
$719$	−8.83915			−0.329645			−0.164822	+	0.986323i	$0.552705\pi$
$720$		0			0
$721$	2.74456			0.102213
$722$	4.76635	+	1.39081i	0.177385	+	0.0517606i
$723$		0			0
$724$		0			0
$725$	25.7648			0.956881
$726$		0			0
$727$			10.4302i			0.386834i	0.981117	+	0.193417i	$0.0619570\pi$
$727$			10.4302i			0.386834i	−0.981117	+	0.193417i	$0.938043\pi$
$728$	16.2912	+	18.6101i	0.603791	+	0.689737i
$729$		0			0
$730$	−5.31386	−	1.55057i	−0.196675	−	0.0573892i
$731$			20.1947i			0.746928i
$732$		0			0
$733$			38.5728i			1.42472i	0.701815	+	0.712359i	$0.252373\pi$
$733$			38.5728i			1.42472i	−0.701815	+	0.712359i	$0.747627\pi$
$734$	−4.39005	+	15.0448i	−0.162040	+	0.555315i
$735$		0			0
$736$	−5.48913	−	36.0211i	−0.202332	−	1.32776i
$737$			13.2665i			0.488678i
$738$		0			0
$739$	−7.25544			−0.266896			−0.133448	−	0.991056i	$-0.542605\pi$
$739$	−7.25544			−0.266896			−0.133448	+	0.991056i	$0.542605\pi$
$740$	−6.06490	+	9.50744i	−0.222950	+	0.349501i
$741$		0			0
$742$	−8.05842	+	27.6165i	−0.295834	+	1.01383i
$743$	17.3020			0.634748			0.317374	−	0.948300i	$-0.397199\pi$
$743$	17.3020			0.634748			0.317374	+	0.948300i	$0.397199\pi$
$744$		0			0
$745$	−9.51087			−0.348451
$746$	1.01082	−	3.46410i	0.0370086	−	0.126830i
$747$		0			0
$748$	−28.2337	−	18.0106i	−1.03233	−	0.658531i
$749$	−16.7966			−0.613734
$750$		0			0
$751$		−	1.02446i		−	0.0373832i	−0.999825	−	0.0186916i	$-0.994050\pi$
$751$		−	1.02446i		−	0.0373832i	0.999825	−	0.0186916i	$-0.00595007\pi$
$752$	18.3128	+	39.3947i	0.667799	+	1.43658i
$753$		0			0
$754$	−5.48913	+	18.8114i	−0.199902	+	0.685071i
$755$			3.90653i			0.142173i
$756$		0			0
$757$			34.1213i			1.24016i	0.784539	+	0.620079i	$0.212900\pi$
$757$			34.1213i			1.24016i	−0.784539	+	0.620079i	$0.787100\pi$
$758$	−12.8824	−	3.75906i	−0.467910	−	0.136535i
$759$		0			0
$760$	−4.46738	−	5.10328i	−0.162049	−	0.185116i
$761$			12.6766i			0.459526i	0.973247	+	0.229763i	$0.0737951\pi$
$761$			12.6766i			0.459526i	−0.973247	+	0.229763i	$0.926205\pi$
$762$		0			0
$763$	−38.2337			−1.38415
$764$	−14.2695	−	9.10268i	−0.516254	−	0.329324i
$765$		0			0
$766$	35.4891	+	10.3556i	1.28227	+	0.374164i
$767$	16.9257			0.611151
$768$		0			0
$769$	−21.7446			−0.784129			−0.392064	−	0.919938i	$-0.628239\pi$
$769$	−21.7446			−0.784129			−0.392064	+	0.919938i	$0.628239\pi$
$770$	−7.79880	−	2.27567i	−0.281049	−	0.0820095i
$771$		0			0
$772$	22.3139	+	14.2342i	0.803093	+	0.512302i
$773$	33.9695			1.22180			0.610898	−	0.791709i	$-0.290808\pi$
$773$	33.9695			1.22180			0.610898	+	0.791709i	$0.290808\pi$
$774$		0			0
$775$		−	28.3662i		−	1.01894i
$776$	−1.86301	−	2.12819i	−0.0668780	−	0.0763977i
$777$		0			0
$778$	31.0367	+	9.05642i	1.11272	+	0.324689i
$779$			8.91754i			0.319504i
$780$		0			0
$781$			14.6581i			0.524507i
$782$	−12.8824	+	44.1485i	−0.460674	+	1.57875i
$783$		0			0
$784$	−8.00000	−	17.2097i	−0.285714	−	0.614632i
$785$		−	2.57924i		−	0.0920570i
$786$		0			0
$787$	1.48913			0.0530816			0.0265408	−	0.999648i	$-0.491551\pi$
$787$	1.48913			0.0530816			0.0265408	+	0.999648i	$0.491551\pi$
$788$	−22.5737	−	14.4000i	−0.804156	−	0.512980i
$789$		0			0
$790$	0.861407	−	2.95207i	0.0306475	−	0.105030i
$791$	41.0452			1.45940
$792$		0			0
$793$	−13.0217			−0.462416
$794$	11.8716	−	40.6844i	0.421307	−	1.44383i
$795$		0			0
$796$	7.29211	−	11.4312i	0.258462	−	0.405170i
$797$	−15.4095			−0.545831			−0.272915	−	0.962038i	$-0.587988\pi$
$797$	−15.4095			−0.545831			−0.272915	+	0.962038i	$0.587988\pi$
$798$		0			0
$799$		−	54.8325i		−	1.93984i
$800$	−4.04326	−	26.5330i	−0.142951	−	0.938083i
$801$		0			0
$802$	1.48913	−	5.10328i	0.0525828	−	0.180203i
$803$		−	25.6858i		−	0.906432i
$804$		0			0
$805$			11.1565i			0.393215i
$806$	20.7107	+	6.04334i	0.729505	+	0.212868i
$807$		0			0
$808$	−29.4090	−	33.5952i	−1.03460	−	1.18187i
$809$			49.8968i			1.75428i	0.480235	+	0.877140i	$0.340551\pi$
$809$			49.8968i			1.75428i	−0.480235	+	0.877140i	$0.659449\pi$
$810$		0			0
$811$	4.74456			0.166604			0.0833021	−	0.996524i	$-0.473453\pi$
$811$	4.74456			0.166604			0.0833021	+	0.996524i	$0.473453\pi$
$812$	20.0172	−	31.3793i	0.702465	−	1.10120i
$813$		0			0
$814$	−50.2337	−	14.6581i	−1.76069	−	0.513765i
$815$	9.21545			0.322803
$816$		0			0
$817$	−18.9783			−0.663965
$818$	14.9336	+	4.35758i	0.522140	+	0.152359i
$819$		0			0
$820$	1.02175	−	1.60171i	0.0356810	−	0.0559342i
$821$	−35.2385			−1.22983			−0.614916	−	0.788593i	$-0.710810\pi$
$821$	−35.2385			−1.22983			−0.614916	+	0.788593i	$0.710810\pi$
$822$		0			0
$823$		−	50.4556i		−	1.75877i	−0.476110	−	0.879386i	$-0.657954\pi$
$823$		−	50.4556i		−	1.75877i	0.476110	−	0.879386i	$-0.342046\pi$
$824$	1.70438	−	1.49200i	0.0593748	−	0.0519763i
$825$		0			0
$826$	−30.8614	−	9.00528i	−1.07381	−	0.313334i
$827$			6.63325i			0.230661i	0.993327	+	0.115330i	$0.0367927\pi$
$827$			6.63325i			0.230661i	−0.993327	+	0.115330i	$0.963207\pi$
$828$		0			0
$829$		−	3.50157i		−	0.121615i	−0.998150	−	0.0608073i	$-0.980632\pi$
$829$		−	3.50157i		−	0.121615i	0.998150	−	0.0608073i	$-0.0193675\pi$
$830$	0.723089	−	2.47805i	0.0250988	−	0.0860144i
$831$		0			0
$832$	20.2337	+	2.70071i	0.701477	+	0.0936304i
$833$			23.9538i			0.829949i
$834$		0			0
$835$	1.02175			0.0353591
$836$	16.9257	−	26.5330i	0.585387	−	0.917663i
$837$		0			0
$838$	2.86141	−	9.80614i	0.0988457	−	0.338747i
$839$	12.5061			0.431759			0.215879	−	0.976420i	$-0.430738\pi$
$839$	12.5061			0.431759			0.215879	+	0.976420i	$0.430738\pi$
$840$		0			0
$841$	0.489125			0.0168664
$842$	10.8608	−	37.2203i	0.374287	−	1.28269i
$843$		0			0
$844$	−21.4891	−	13.7081i	−0.739686	−	0.471854i
$845$	−3.27966			−0.112824
$846$		0			0
$847$		0			0
$848$	10.0086	+	21.5306i	0.343696	+	0.739364i
$849$		0			0
$850$	−9.48913	+	32.5196i	−0.325474	+	1.11541i
$851$			71.8613i			2.46337i
$852$		0			0
$853$			6.70500i			0.229575i	0.993390	+	0.114787i	$0.0366187\pi$
$853$			6.70500i			0.229575i	−0.993390	+	0.114787i	$0.963381\pi$
$854$	23.7432	+	6.92820i	0.812475	+	0.237078i
$855$		0			0
$856$	−10.4307	+	9.13096i	−0.356514	+	0.312090i
$857$		−	2.46943i		−	0.0843543i	−0.999110	−	0.0421771i	$-0.986571\pi$
$857$		−	2.46943i		−	0.0843543i	0.999110	−	0.0421771i	$-0.0134294\pi$
$858$		0			0
$859$	−20.4674			−0.698338			−0.349169	−	0.937060i	$-0.613536\pi$
$859$	−20.4674			−0.698338			−0.349169	+	0.937060i	$0.613536\pi$
$860$	3.40876	+	2.17448i	0.116238	+	0.0741492i
$861$		0			0
$862$	20.2337	+	5.90414i	0.689162	+	0.201096i
$863$	−26.5174			−0.902664			−0.451332	−	0.892356i	$-0.649051\pi$
$863$	−26.5174			−0.902664			−0.451332	+	0.892356i	$0.649051\pi$
$864$		0			0
$865$	5.74456			0.195321
$866$	−25.1008	−	7.32435i	−0.852959	−	0.248891i
$867$		0			0
$868$	−34.5475	−	22.0382i	−1.17262	−	0.748027i
$869$	14.2695			0.484061
$870$		0			0
$871$			10.2066i			0.345836i
$872$	−23.7432	+	20.7846i	−0.804046	+	0.703856i
$873$		0			0
$874$	−41.4891	−	12.1064i	−1.40339	−	0.409506i
$875$			16.8781i			0.570583i
$876$		0			0
$877$		−	13.7081i		−	0.462891i	−0.972848	−	0.231445i	$-0.925655\pi$
$877$		−	13.7081i		−	0.462891i	0.972848	−	0.231445i	$-0.0743455\pi$
$878$	−7.42249	+	25.4371i	−0.250497	+	0.858462i
$879$		0			0
$880$	−6.08017	+	2.82639i	−0.204963	+	0.0952776i
$881$		−	7.62792i		−	0.256991i	−0.991710	−	0.128496i	$-0.958985\pi$
$881$		−	7.62792i		−	0.256991i	0.991710	−	0.128496i	$-0.0410148\pi$
$882$		0			0
$883$	−23.7228			−0.798336			−0.399168	−	0.916878i	$-0.630701\pi$
$883$	−23.7228			−0.798336			−0.399168	+	0.916878i	$0.630701\pi$
$884$	−21.7216	−	13.8564i	−0.730575	−	0.466041i
$885$		0			0
$886$	−2.62772	+	9.00528i	−0.0882799	+	0.302538i
$887$	−9.21545			−0.309425			−0.154712	−	0.987960i	$-0.549445\pi$
$887$	−9.21545			−0.309425			−0.154712	+	0.987960i	$0.549445\pi$
$888$		0			0
$889$	35.2337			1.18170
$890$	3.40876	−	11.6819i	0.114262	−	0.391579i
$891$		0			0
$892$	19.3723	−	30.3683i	0.648632	−	1.01681i
$893$	51.5296			1.72437
$894$		0			0
$895$		−	5.97868i		−	0.199845i
$896$	−35.4562	−	15.6896i	−1.18451	−	0.524154i
$897$		0			0
$898$	−1.76631	+	6.05321i	−0.0589426	+	0.201998i
$899$		−	32.4665i		−	1.08282i
$900$		0			0
$901$		−	29.9679i		−	0.998376i
$902$	8.46284	+	2.46943i	0.281782	+	0.0822232i
$903$		0			0
$904$	25.4891	−	22.3130i	0.847756	−	0.742119i
$905$		0			0
$906$		0			0
$907$	−54.2337			−1.80080			−0.900400	−	0.435063i	$-0.856726\pi$
$907$	−54.2337			−1.80080			−0.900400	+	0.435063i	$0.856726\pi$
$908$	25.4476	−	39.8921i	0.844507	−	1.32386i
$909$		0			0
$910$	−6.00000	−	1.75079i	−0.198898	−	0.0580380i
$911$	10.8608			0.359834			0.179917	−	0.983682i	$-0.442417\pi$
$911$	10.8608			0.359834			0.179917	+	0.983682i	$0.442417\pi$
$912$		0			0
$913$	11.9783			0.396422
$914$	−56.2960	−	16.4270i	−1.86211	−	0.543358i
$915$		0			0
$916$	−9.25544	+	14.5090i	−0.305808	+	0.479391i
$917$	6.94661			0.229397
$918$		0			0
$919$			26.6900i			0.880420i	0.897895	+	0.440210i	$0.145096\pi$
$919$			26.6900i			0.880420i	−0.897895	+	0.440210i	$0.854904\pi$
$920$	6.06490	+	6.92820i	0.199954	+	0.228416i
$921$		0			0
$922$	46.8030	+	13.6570i	1.54137	+	0.449769i
$923$			11.2772i			0.371192i
$924$		0			0
$925$			52.9327i			1.74042i
$926$	12.5356	−	42.9600i	0.411946	−	1.41175i
$927$		0			0
$928$	−4.62772	−	30.3683i	−0.151912	−	0.996890i
$929$			42.9686i			1.40976i	0.709329	+	0.704878i	$0.248998\pi$
$929$			42.9686i			1.40976i	−0.709329	+	0.704878i	$0.751002\pi$
$930$		0			0
$931$	−22.5109			−0.737764
$932$	−0.634508	+	0.994667i	−0.0207840	+	0.0325814i
$933$		0			0
$934$	−12.4090	+	42.5259i	−0.406033	+	1.39149i
$935$	8.46284			0.276764
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	5.43039	−	18.6101i	0.177308	−	0.607642i
$939$		0			0
$940$	−9.25544	−	5.90414i	−0.301879	−	0.192572i
$941$	3.91416			0.127598			0.0637991	−	0.997963i	$-0.479678\pi$
$941$	3.91416			0.127598			0.0637991	+	0.997963i	$0.479678\pi$
$942$		0			0
$943$		−	12.1064i		−	0.394239i
$944$	−24.0604	+	11.1846i	−0.783101	+	0.364027i
$945$		0			0
$946$	−5.25544	+	18.0106i	−0.170869	+	0.585574i
$947$			11.8294i			0.384404i	0.981355	+	0.192202i	$0.0615629\pi$
$947$			11.8294i			0.384404i	−0.981355	+	0.192202i	$0.938437\pi$
$948$		0			0
$949$		−	19.7613i		−	0.641481i
$950$	−30.5607	−	8.91754i	−0.991520	−	0.289323i
$951$		0			0
$952$	32.2337	+	36.8220i	1.04470	+	1.19341i
$953$		−	31.4719i		−	1.01947i	−0.860330	−	0.509737i	$-0.829743\pi$
$953$		−	31.4719i		−	1.01947i	0.860330	−	0.509737i	$-0.170257\pi$
$954$		0			0
$955$	4.27719			0.138407
$956$	−25.7648	−	16.4356i	−0.833294	−	0.531567i
$957$		0			0
$958$	2.74456	+	0.800857i	0.0886728	+	0.0258745i
$959$	−58.3472			−1.88413
$960$		0			0
$961$	−4.74456			−0.153050
$962$	−38.6472	−	11.2772i	−1.24604	−	0.363590i
$963$		0			0
$964$	3.37228	+	2.15121i	0.108614	+	0.0692859i
$965$	−6.68841			−0.215308
$966$		0			0
$967$		−	12.8327i		−	0.412673i	−0.978481	−	0.206337i	$-0.933846\pi$
$967$		−	12.8327i		−	0.412673i	0.978481	−	0.206337i	$-0.0661542\pi$
$968$		0			0
$969$		0			0
$970$	0.686141	+	0.200214i	0.0220306	+	0.00642849i
$971$		−	14.5938i		−	0.468337i	−0.972196	−	0.234169i	$-0.924763\pi$
$971$		−	14.5938i		−	0.468337i	0.972196	−	0.234169i	$-0.0752367\pi$
$972$		0			0
$973$			27.4163i			0.878925i
$974$	−3.72601	+	12.7692i	−0.119389	+	0.409150i
$975$		0			0
$976$	18.5109	−	8.60485i	0.592519	−	0.275435i
$977$			47.3176i			1.51382i	0.653517	+	0.756912i	$0.273293\pi$
$977$			47.3176i			1.51382i	−0.653517	+	0.756912i	$0.726707\pi$
$978$		0			0
$979$	56.4674			1.80471
$980$	4.04326	+	2.57924i	0.129157	+	0.0823908i
$981$		0			0
$982$	11.0802	−	37.9721i	0.353582	−	1.21174i
$983$	28.5391			0.910255			0.455127	−	0.890426i	$-0.349594\pi$
$983$	28.5391			0.910255			0.455127	+	0.890426i	$0.349594\pi$
$984$		0			0
$985$	6.76631			0.215593
$986$	−10.8608	+	37.2203i	−0.345878	+	1.18533i
$987$		0			0
$988$	13.0217	−	20.4131i	0.414277	−	0.649428i
$989$	25.7648			0.819274
$990$		0			0
$991$			12.0319i			0.382205i	0.981570	+	0.191103i	$0.0612064\pi$
$991$			12.0319i			0.382205i	−0.981570	+	0.191103i	$0.938794\pi$
$992$	−33.4345	+	5.09496i	−1.06155	+	0.161765i
$993$		0			0
$994$	6.00000	−	20.5622i	0.190308	−	0.652194i
$995$			3.42643i			0.108625i
$996$		0			0
$997$			31.8678i			1.00926i	0.863335	+	0.504631i	$0.168372\pi$
$997$			31.8678i			1.00926i	−0.863335	+	0.504631i	$0.831628\pi$
$998$	−38.0127	−	11.0920i	−1.20327	−	0.351112i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.f.b.107.8	yes	8
3.2	odd	2	inner	216.2.f.b.107.1	✓	8
4.3	odd	2		864.2.f.b.431.3		8
8.3	odd	2	inner	216.2.f.b.107.2	yes	8
8.5	even	2		864.2.f.b.431.6		8
9.2	odd	6		648.2.l.e.539.2		8
9.4	even	3		648.2.l.e.107.1		8
9.5	odd	6		648.2.l.d.107.4		8
9.7	even	3		648.2.l.d.539.3		8
12.11	even	2		864.2.f.b.431.5		8
24.5	odd	2		864.2.f.b.431.4		8
24.11	even	2	inner	216.2.f.b.107.7	yes	8
36.7	odd	6		2592.2.p.d.2159.3		8
36.11	even	6		2592.2.p.e.2159.2		8
36.23	even	6		2592.2.p.d.431.2		8
36.31	odd	6		2592.2.p.e.431.3		8
72.5	odd	6		2592.2.p.d.431.3		8
72.11	even	6		648.2.l.e.539.1		8
72.13	even	6		2592.2.p.e.431.2		8
72.29	odd	6		2592.2.p.e.2159.3		8
72.43	odd	6		648.2.l.d.539.4		8
72.59	even	6		648.2.l.d.107.3		8
72.61	even	6		2592.2.p.d.2159.2		8
72.67	odd	6		648.2.l.e.107.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.b.107.1	✓	8	3.2	odd	2	inner
216.2.f.b.107.2	yes	8	8.3	odd	2	inner
216.2.f.b.107.7	yes	8	24.11	even	2	inner
216.2.f.b.107.8	yes	8	1.1	even	1	trivial
648.2.l.d.107.3		8	72.59	even	6
648.2.l.d.107.4		8	9.5	odd	6
648.2.l.d.539.3		8	9.7	even	3
648.2.l.d.539.4		8	72.43	odd	6
648.2.l.e.107.1		8	9.4	even	3
648.2.l.e.107.2		8	72.67	odd	6
648.2.l.e.539.1		8	72.11	even	6
648.2.l.e.539.2		8	9.2	odd	6
864.2.f.b.431.3		8	4.3	odd	2
864.2.f.b.431.4		8	24.5	odd	2
864.2.f.b.431.5		8	12.11	even	2
864.2.f.b.431.6		8	8.5	even	2
2592.2.p.d.431.2		8	36.23	even	6
2592.2.p.d.431.3		8	72.5	odd	6
2592.2.p.d.2159.2		8	72.61	even	6
2592.2.p.d.2159.3		8	36.7	odd	6
2592.2.p.e.431.2		8	72.13	even	6
2592.2.p.e.431.3		8	36.31	odd	6
2592.2.p.e.2159.2		8	36.11	even	6
2592.2.p.e.2159.3		8	72.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35760 + 0.396143i) q^{2} +(1.68614 + 1.07561i) q^{4} -0.505408 q^{5} +3.42703i q^{7} +(1.86301 + 2.12819i) q^{8} +O(q^{10})\)	\(q+(1.35760 + 0.396143i) q^{2} +(1.68614 + 1.07561i) q^{4} -0.505408 q^{5} +3.42703i q^{7} +(1.86301 + 2.12819i) q^{8} +(-0.686141 - 0.200214i) q^{10} -3.31662i q^{11} -2.55164i q^{13} +(-1.35760 + 4.65253i) q^{14} +(1.68614 + 3.62725i) q^{16} -5.04868i q^{17} +4.74456 q^{19} +(-0.852189 - 0.543620i) q^{20} +(1.31386 - 4.50264i) q^{22} -6.44121 q^{23} -4.74456 q^{25} +(1.01082 - 3.46410i) q^{26} +(-3.68614 + 5.77846i) q^{28} -5.43039 q^{29} +5.97868i q^{31} +(0.852189 + 5.59230i) q^{32} +(2.00000 - 6.85407i) q^{34} -1.73205i q^{35} -11.1565i q^{37} +(6.44121 + 1.87953i) q^{38} +(-0.941578 - 1.07561i) q^{40} +1.87953i q^{41} -4.00000 q^{43} +(3.56738 - 5.59230i) q^{44} +(-8.74456 - 2.55164i) q^{46} +10.8608 q^{47} -4.74456 q^{49} +(-6.44121 - 1.87953i) q^{50} +(2.74456 - 4.30243i) q^{52} +5.93580 q^{53} +1.67625i q^{55} +(-7.29339 + 6.38458i) q^{56} +(-7.37228 - 2.15121i) q^{58} +6.63325i q^{59} -5.10328i q^{61} +(-2.36841 + 8.11663i) q^{62} +(-1.05842 + 7.92967i) q^{64} +1.28962i q^{65} -4.00000 q^{67} +(5.43039 - 8.51278i) q^{68} +(0.686141 - 2.35143i) q^{70} -4.41957 q^{71} +7.74456 q^{73} +(4.41957 - 15.1460i) q^{74} +(8.00000 + 5.10328i) q^{76} +11.3662 q^{77} +4.30243i q^{79} +(-0.852189 - 1.83324i) q^{80} +(-0.744563 + 2.55164i) q^{82} +3.61158i q^{83} +2.55164i q^{85} +(-5.43039 - 1.58457i) q^{86} +(7.05842 - 6.17889i) q^{88} +17.0256i q^{89} +8.74456 q^{91} +(-10.8608 - 6.92820i) q^{92} +(14.7446 + 4.30243i) q^{94} -2.39794 q^{95} -1.00000 q^{97} +(-6.44121 - 1.87953i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4}+O(q^{10}) \) 8 * q + 2 * q^4	\( 8 q + 2 q^{4} + 6 q^{10} + 2 q^{16} - 8 q^{19} + 22 q^{22} + 8 q^{25} - 18 q^{28} + 16 q^{34} - 42 q^{40} - 32 q^{43} - 24 q^{46} + 8 q^{49} - 24 q^{52} - 36 q^{58} + 26 q^{64} - 32 q^{67} - 6 q^{70} + 16 q^{73} + 64 q^{76} + 40 q^{82} + 22 q^{88} + 24 q^{91} + 72 q^{94} - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 + 6 * q^10 + 2 * q^16 - 8 * q^19 + 22 * q^22 + 8 * q^25 - 18 * q^28 + 16 * q^34 - 42 * q^40 - 32 * q^43 - 24 * q^46 + 8 * q^49 - 24 * q^52 - 36 * q^58 + 26 * q^64 - 32 * q^67 - 6 * q^70 + 16 * q^73 + 64 * q^76 + 40 * q^82 + 22 * q^88 + 24 * q^91 + 72 * q^94 - 8 * q^97

Introduction

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